Homework: Section 13.2 Homework Score: 0 of 1 pt 13.2.35 Save 9of21 (0complete)

Question

Homework: Section 13.2 Homework Score: 0 of 1 pt 13.2.35 Save 9of21 (0complete) HW Score: 0%, 0 of 21 pts Question Help a Give a geometric description of the following set of points. x2y 2-6x-14y 12z s63 Choose the correct answer below O A. A ball with center (3,7.6) and radius157 O B. Aball with center (3,7.6) and radius 157 OC. Aball with center(-3.-7,-6) and radius 157 O D. A ball with center (-3,-7,-6) and radius /157 O E. The entire xyz-coordinate system O F. The empty xyz-coordinate system

Explanation / Answer

x^2+y^2+z^2-6x-14y-12z <= 63

x^2-6x+9 + y^2-14y+49+z^2-12z+36<= 63+9+49+36

(x-3)^2+(y-7)^2+(z-6)^2 <= 157

(x-3)^2+(y-7)^2+(z-6)^2 <= (sqrt(157))^2

In general, for sphere with center (a,b,c) and radius r equation is

(x-a)^2+(y-b)^2+(z-c)^2 <= r^2

Thus, comparing we get

Center is (3,7,6) and radius is sqrt(157)

Option 1

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